DG singular equivalence and singular locus
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915250331189248 |
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| author | Liu, Leilei Zeng, Jieheng |
| author_facet | Liu, Leilei Zeng, Jieheng |
| contents | For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from DG singularity category $S_{dg}(R)$ of $R$ such that there is a finite surjective morphism $X \rightarrow \mathrm{Spec}(R /I)$, where $\mathrm{Spec}(R /I)$ is the singular locus in $\mathrm{Spec}(R)$. As an application, for two such rings with equivalent DG singularity categories, we prove that the singular loci in their affine schemes have the same dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DG singular equivalence and singular locus Liu, Leilei Zeng, Jieheng Commutative Algebra Algebraic Geometry Rings and Algebras Representation Theory For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from DG singularity category $S_{dg}(R)$ of $R$ such that there is a finite surjective morphism $X \rightarrow \mathrm{Spec}(R /I)$, where $\mathrm{Spec}(R /I)$ is the singular locus in $\mathrm{Spec}(R)$. As an application, for two such rings with equivalent DG singularity categories, we prove that the singular loci in their affine schemes have the same dimension. |
| title | DG singular equivalence and singular locus |
| topic | Commutative Algebra Algebraic Geometry Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2403.13637 |